Impossibility of phylogeny reconstruction from $k$-mer counts

TL;DR

This paper proves that using only $k$-mer counts from full sequences is insufficient for consistent phylogeny reconstruction under a two-state model, highlighting the need for more advanced methods.

Contribution

It establishes a fundamental impossibility result showing that $k$-mer counts alone cannot reliably reconstruct phylogenies, emphasizing the necessity for more sophisticated approaches.

Findings

No consistent phylogeny estimation from $k$-mer counts alone for fixed $k$

Joint distributions of $k$-mer counts on different trees are statistically indistinguishable asymptotically

Statistical consistency requires additional techniques beyond simple $k$-mer counts

Abstract

We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed $k$ no statistically consistent phylogeny estimation is possible from $k$-mer counts over the full leaf sequences alone. Formally, we establish that the joint distribution of $k$-mer counts over the entire leaf sequences on two distinct trees have total variation distance bounded away from $1$ as the sequence length tends to infinity. Our impossibility result implies that statistical consistency requires more sophisticated use of $k$-mer count information, such as block techniques developed in previous theoretical work.